Geodesic
Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 483-508

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Let $\Delta$ be thick affine building of type $\widetilde{G}_{2}$ the Laplace operators of $\Delta$; associated with a pair $(y_{1}, y_{2})$; is the Poisson transform of a suitable finitely additive measure on the maximal boundary $\Omega$ of $\Delta$; by using only the combinatorial structure of $\Delta$. 
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     author = {Mantero, A. M. and Zappa, A.},
     title = {Eigenfunctions of the {Laplace} {Operators} for a {Building} of {Type} $\widetilde{G}_{2}$},
     journal = {Bollettino della Unione matematica italiana},
     pages = {483--508},
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     volume = {Ser. 9, 2},
     number = {2},
     year = {2009},
     zbl = {1181.43004},
     mrnumber = {2537284},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a12/}
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Mantero, A. M.; Zappa, A. Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 483-508. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a12/